|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
orthogonal group
|
|
gptkbp:actsOn
|
R^n
|
|
gptkbp:centralTo
|
{I, -I} for even n
{I} for odd n
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:consistsOf
|
n x n orthogonal matrices with determinant 1
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
n(n-1)/2
|
|
gptkbp:fundamentalGroup
|
Z for n = 2
Z_2 for n >= 3
trivial for n = 1
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:O(n,_R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SO(n, R)
|
|
gptkbp:identityElement
|
identity matrix
|
|
gptkbp:isNonAbelian
|
true for n = 1
true for n >= 3
|
|
gptkbp:isSimple
|
n >= 5
true for n >= 5
|
|
gptkbp:Lie_algebra
|
so(n, R)
|
|
gptkbp:notation
|
gptkb:SO(n)
gptkb:SO(n,_R)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:preserves
|
gptkb:Euclidean_inner_product
orientation
|
|
gptkbp:realization
|
group of rotations in n-dimensional space
|
|
gptkbp:relatedTo
|
gptkb:rotation_group
gptkb:Spin_group
orthogonal group
|
|
gptkbp:universalCover
|
gptkb:Spin(n)
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:theoretical_physics
computer graphics
differential geometry
engineering
physics
representation theory
robotics
|
|
gptkbp:bfsParent
|
gptkb:orthogonal_group
|
|
gptkbp:bfsLayer
|
5
|